Problem with SDP

I’m trying to solve large SDP problem (1000X1000) with about 10-50 constraints. The problems themselves are not “hard” (it’s easy to find a feasible solution).
The problem’s solution takes a very long time, I think most of it on the actual modeling for some reason, though I cannot verify it, since I understand there is no method to measure them separately. In any case it gives me a solved status, but the solution is incorrect, the objective function value is 1.4 the real optimal value, and the matrix is not PSD (maximum eigenvalue ~20 minimal ~-0.1), the result were achieved when setting the precision to ‘high’.
Is this a bug or a solver or modeling accuracy issue?
I tried solving smaller problems (100X100) and there was no problem.

off topic: Is there a way to record solver time separately?